Measurement of the Higgs boson mass in the H  →  Z Z ⁎  → 4 ℓ and H  →  γγ channels with √s = 13 TeV pp collisions using the ATLAS detector

Article

Reference

Measurement of the Higgs boson mass in the H  →  Z Z ⁎  → 4 ℓ and H  →  γγ channels with √s = 13 TeV pp collisions using the

ATLAS detector

ATLAS Collaboration AKILLI, Ece (Collab.), et al .

Abstract

The mass of the Higgs boson is measured in the H→ZZ⁎→4ℓ and in the H→γγ decay channels with 36.1 fb −1 of proton–proton collision data from the Large Hadron Collider at a centre-of-mass energy of 13 TeV recorded by the ATLAS detector in 2015 and 2016. The measured value in the H→ZZ⁎→4ℓ channel is mHZZ⁎=124.79±0.37GeV , while the measured value in the H→γγ channel is mHγγ=124.93±0.40GeV . Combining these results with the ATLAS measurement based on 7 and 8 TeV proton–proton collision data yields a Higgs boson mass of mH=124.97±0.24GeV .

ATLAS Collaboration, AKILLI, Ece (Collab.), et al . Measurement of the Higgs boson mass in the H  →  Z Z ⁎  → 4 ℓ and H  →  γγ channels with √s = 13 TeV pp collisions using the ATLAS detector. Physics Letters. B , 2018

DOI : 10.1016/j.physletb.2018.07.050

Available at:

http://archive-ouverte.unige.ch/unige:107322

Disclaimer: layout of this document may differ from the published version.

1 / 1

Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Measurement of the Higgs boson mass in the H → ^{Z Z ∗} → ⁴ and H → γ γ channels with √

s = ^{13 TeV pp collisions using the ATLAS} detector

.The ATLAS Collaboration

a r t i c l e i n f o a b s t ra c t

Articlehistory:

Received4June2018

Receivedinrevisedform20July2018 Accepted27July2018

Availableonline2August2018 Editor: M. Doser

Themass oftheHiggsbosonismeasuredinthe H→^{Z Z∗}→⁴andinthe H→γ γ decaychannels with 36.1 fb⁻¹ of proton–proton collision data from the Large Hadron Collider at a centre-of-mass energy of 13 TeV recorded by the ATLAS detector in 2015 and 2016. The measured value in the H→^{Z Z∗}→⁴channelism^{Z Z}_H ^∗=¹²⁴.79±⁰.37 GeV,whilethemeasuredvalueintheH→γ γ channel ism^{γ γ}_H =¹²⁴.93±⁰.40 GeV.CombiningtheseresultswiththeATLASmeasurementbasedon7and8 TeV proton–protoncollisiondatayieldsaHiggsbosonmassofmH=¹²⁴.97±⁰.24 GeV.

©^{2018TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense} (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

The observationof a Higgs boson, H,by the ATLAS andCMS experiments [1,2] with the Large Hadron Collider (LHC) Run 1 proton–proton (pp) collision data at centre-of-mass energies of

√s= ^{7 and 8 TeV was a major step towards} understanding the mechanism of electroweak (EW) symmetry breaking [3–5]. The massoftheHiggsbosonwasmeasuredtobe125.09±⁰.24 GeV [6]

basedonthecombinedRun 1datasamplesoftheATLASandCMS Collaborations, who also reportedindividual mass measurements inRefs. [7,8].Recently,theCMSCollaborationmeasuredtheHiggs boson mass in the H→^{Z Z∗}→⁴ channel using 35.9 fb⁻¹ of 13 TeV pp collision data [9]. The measured value of themass is 125.26±⁰.21 GeV.

ThisLetter presentsa measurement ofthe Higgs bosonmass, mH,with36.1 fb⁻¹ of√

s=^{13 TeVppcollisiondatarecordedwith} theATLASdetector.Themeasurementisderivedfromacombined fitto the four-leptonand diphotoninvariant mass spectra inthe decaychannelsH→^{Z Z∗}→⁴(=^e,

μ

)andH→

γ γ

.Acombi- nationwiththeATLASRun 1dataisalsopresented.

2. ATLASdetector

TheATLASexperiment [10] attheLHCisamulti-purposepar- ticledetectorwithnearly 4

π

coverage insolid angle.¹ It consists

E-mailaddress:atlas.publications@cern.ch.

1 ATLASusesaright-handedcoordinatesystemwithitsoriginatthe nominal interactionpoint(IP)inthecentreofthedetectorandthez-axisalongthebeam pipe.Thex-axispointsfromtheIPtothecentreoftheLHCring,andthe y-axis

ofan inner trackingdetector(ID)surrounded bya 2 Tsupercon- ductingsolenoid,electromagnetic(EM)andhadroniccalorimeters, and a muon spectrometer (MS) incorporating three large super- conductingtoroidalmagnets.TheIDprovidestrackingforcharged particlesfor|

η

|<2.5.Thecalorimetersystemcovers thepseudo- rapidityrange|

η

|<4.9.Itselectromagneticpartissegmentedinto threeshower-depthlayersfor|

η

_|<2.5 andincludesapresampler for |

η

_|<1.8. The MS includes high-precision tracking chambers (|

η

|<2.7) andfasttriggerchambers(|

η

|<2.4). Onlineeventse- lectionisperformedbya first-leveltriggerwithamaximumrate of 100 kHz, implemented in custom electronics, followed by a software-basedhigh-leveltriggerwithamaximumrateof1kHz.

3. Dataandsimulatedsamples

Thismeasurementuses datafrom ppcollisions withacentre- of-massenergy of 13 TeV collected during 2015 and2016 using single-lepton,dilepton,trileptonanddiphotontriggers,withlooser identification, isolation and transverse momentum (pT) require- ments than those applied offline.The combined efficiencyof the lepton triggers is about 98% for the H→^{Z Z∗}→⁴ events (as- sumingmH=^{125 GeV)passingtheofflineselection.Thediphoton} triggerefficiencyis higherthan99% forselected H→

γ γ

events (assumingmH=^{125 GeV).Aftertriggerand}data-qualityrequire- ments, theintegratedluminosity ofthedatasample is 36.1 fb⁻¹.

pointsupwards.Cylindricalcoordinates(r,φ)areusedinthetransverseplane,φ beingtheazimuthalanglearoundthez-axis.Thepseudorapidityisdefinedinterms ofthepolarangleθasη= −ln tan(θ/2).Angulardistanceismeasuredinunitsof

R≡

( η)²+( φ)². https://doi.org/10.1016/j.physletb.2018.07.050

0370-2693/©^{2018TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense}(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

Themeannumberofproton–protoninteractionsperbunch cross- ing (integrated luminosity) is14 (3.2 fb⁻¹) inthe 2015 dataset and25(32.9 fb⁻¹)inthe2016dataset.

MonteCarlo(MC) simulationis usedinthe analysisto model thedetectorresponseforsignalandbackgroundprocesses.Forthe H→^{Z Z∗}→⁴measurement,adetailedlistanddescriptionofthe MC-simulatedsamplesused canbe foundinRef. [11] and onlya few differencesspecificto themass analysisarementioned here.

Forthegluon–gluonfusion (ggF)signal,theNNLOPS samplegen- erated atnext-to-next-to-leading order(NNLO) in QCD [12] with mH=¹²³, 125, 126GeV and thePDF4LHC NLO parton distribu- tion function (PDF) set [13] wasused.Additional samples gener- atedatdifferentm_H values(120,122,124,125,126,128,130 GeV) atnext-to-leadingorder(NLO)were alsoused.TheNLO ggFsim- ulation was performed with Powheg-Box v2 [14] interfaced to Pythia8 [15] forpartonshoweringandhadronisation,andtoEvt- Gen[16] forthesimulationofb-hadrondecays.TheCT10NLO [17]

PDF setwas usedfor thehard process andthe CTEQ6L1 [18] set forthepartonshower.Thenon-perturbativeeffectsweremodelled usingtheAZNLOsetoftunedparameters [19].

The Z Z^∗ continuum backgroundfromquark–antiquarkannihi- lation was modelled at NLO in QCD using Powheg-Box v2 and interfacedtoPythia8forpartonshoweringandhadronisation,and to EvtGenfor b-hadrondecays.The PDF set usedis thesame as for the NLO ggF signal. NNLO QCD [20,21] and NLO EW correc- tions [22,23] wereapplied asa functionof theinvariant mass of the Z Z^∗ system(mZ Z^∗).

FortheH→

γ γ

measurement,thesameH→

γ γ

signal(gen- eratedform_H =^{125 GeV)andbackgroundsimulatedeventsused} for the measurements of the Higgs boson couplings andfiducial cross-sections inthe diphoton final state [24] were used. In ad- dition,signal sampleswithalternative mH values(110, 122,123, 124,126,127, 130,140 GeV) wereproduced,withthesamegen- eratorsand settings asthe mH=125 GeV samples, but only for thefourHiggsbosonproductionmodeswithlargestcross-section:

gluon–gluonfusion,vector–bosonfusion(VBF),andassociatedpro- ductionwith avector boson V =^W,Z (V H), forqq¯→^{V H and} gg→^{Z H. For rarer processes, such as associated production of} theHiggsbosonwithatop-quarkpair(tt H¯ )orasingletop-quark (t H), contributingto lessthan 2% ofthe total cross-section,only samplesatmH=125 GeV wereused.

Except for the

γ γ

background sample, whose modelling re- quiresalargeMCsample obtainedthroughafastparametricsim- ulationofthecalorimeterresponse [25], thegeneratedeventsfor allprocesseswerepassedthroughaGeant4 [26] simulationofthe responseof theATLAS detector [25].Forboth detectoremulation methods,eventswere reconstructed withthe samealgorithms as thedata.Additional proton–protoninteractions (pile-up)were in- cludedinboththeparametricandtheGeant4simulations,match- ingtheaveragenumberofinteractionsperLHCbunchcrossingto thespectrumobservedinthedata.

TheStandardModel(SM)expectationsfortheHiggsbosonpro- ductioncross-sectiontimesbranchingratio,inthevariousproduc- tionmodesandfinalstatesunderstudyandateachvalue ofmH, were taken from Refs. [27–30] and used to normalise the simu- latedsamples,asdescribedinRefs. [11,24].

4. Muonreconstruction,identificationandcalibration

Muon trackreconstructionis firstperformedindependentlyin the ID and the MS. Hit information from the individual subde- tectors is then used in a combined muon reconstruction, which includesinformationfromthecalorimeters.

Correctionstothereconstructedmomentumare appliedinor- der to matchthe simulation to data precisely. These corrections

to thesimulatedmomentumresolutionandmomentumscaleare parameterisedasapowerexpansioninthemuonpT,witheachco- efficientmeasuredseparatelyfortheIDandMS,asafunctionof

η

andφ,fromlargedatasamplesof J/ψ→

μ

⁺

μ

⁻and Z→

μ

⁺

μ

⁻

decays. Thescale correctionsrange from0.1% to 0.5% forthe pT ofmuonsoriginatingfrom J/ψ→

μ

⁺

μ

⁻ and Z→

μ

⁺

μ

⁻ decays andaccountforinaccuratemeasurementoftheenergylostinthe traversedmaterial,localmagneticfieldinaccuraciesandgeometri- caldistortions.Thecorrectionstothemuonmomentumresolution formuonsfrom J/ψ→

μ

⁺

μ

⁻andZ→

μ

⁺

μ

⁻areatthepercent level. After detectoralignment, there are residual local misalign- ments that bias the muon tracksagitta, leaving thetrack

χ

² in- variant [31,32],andintroduceasmallcharge-dependentresolution degradation. Thebias inthemeasured momentum ofeachmuon is corrected by an iterative procedure derived from Z→

μ

⁺

μ

⁻

decaysandcheckedagainstthe E/pratiomeasuredin Z→e⁺e⁻ decays. The residual effectafter correction is reduced to theper mille levelat thescale ofthe Z boson mass.Thiscorrection im- proves the resolution of the dimuon invariant mass in Z boson decaysby1%to5%,depending on

η

andφ ofthemuon.Thesys- tematicuncertaintyassociatedwiththiscorrectionisestimatedfor each muonusingsimulationandisfoundtobe about0.4×¹⁰⁻³ fortheaveragemomentumofmuonsfrom Z→

μ

⁺

μ

⁻ decays.

For muons from Z →

μ

⁺

μ

⁻ decays, with momenta ofabout 45 GeV,themomentumscaleisdeterminedtoaprecisionof0.05%

for muonswith|

η

|<2,and about0.2% formuonswith |

η

|≥^2.

Similarly, the resolutionis known with a precision ranging from 1% to2%formuonswith|

η

_|<2 andaround10%formuonswith

|

η

|≥^{2 [33].Boththemomentumscaleandmomentumresolution} uncertaintiesinthecorrectionstosimulationaretakenasfullycor- relatedbetweentheRun1andRun2measurements.

5. Photonandelectronreconstruction,identificationand calibration

Photon and electron candidates are reconstructed from clus- ters of electromagnetic calorimeter cells [34]. Clusters without a matchingtrackorreconstructedconversionvertexintheinnerde- tector areclassifiedasunconvertedphotons.Those withamatch- ingreconstructedconversionvertexoramatchingtrack,consistent with originatingfroma photon conversion, are classifiedascon- verted photons [35]. Clusters matched to a trackconsistent with originatingfroman electron(based on transitionradiation inthe ID)produced inthe beaminteractionregion areconsidered elec- troncandidates.

The energymeasurement forreconstructed electronsandpho- tonsis performedby summingthe energiesmeasured inthe EM calorimetercellsbelongingtothecandidatecluster.Theenergyis measured fromaclustersize of

η

× φ=⁰.075×⁰.175 inthe barrel region of the calorimeter and

η

_× φ=⁰.125×⁰.125 in the calorimeter endcaps. The procedure for the energy mea- surement of electrons and photons closely follows that used in Run 1 [36],withupdatestoreflectthe2015and2016data-taking conditions:

•^{Thedifferentlayersofthe}electromagneticcalorimeterarein- tercalibrated by applying methods similar tothose described in Ref. [36]. The first and second calorimeter layers are in- tercalibratedusingtheenergydepositedbymuonsfrom Z→

μ

⁺

μ

⁻decays,withatypicaluncertaintyof0.7%to1.5%(1.5%

to 2.5%) as a function of

η

in the barrel (endcap) calorime- ter, for |

η

|<2.4. This uncertaintyis added in quadrature to the uncertainty in the modelling of the muon ionisation in thesimulation(1%to1.5%depending on

η

).Theenergyscale ofthe presamplerisestimatedusingelectrons from Z boson

decays,aftercorrectingthesimulationonthebasisofthecor- relations between the amount of detector material and the ratio ofthe energies depositedin thefirst andsecond layers of thecalorimeter. The uncertaintyin thepresamplerenergy scalevariesbetween1.5%and3%dependingon

η

.

•^{The clusterenergyiscorrectedforenergylossintheinactive} materialsinfrontofthecalorimeter,thefractionofenergyde- posited outsidethearea ofthe clusterin the

η

–φ plane, the amountofenergylostbehindtheelectromagneticcalorimeter, and toaccount forthe variation ofthe energyresponse asa functionoftheimpactpointinthecalorimeter.Thecalibration coefficientsusedtoapplythesecorrectionsareobtainedfrom adetailedsimulationofthedetectorresponsetoelectronsand photons,andareoptimisedwithaboosteddecisiontree(BDT).

Thealgorithm,describedinRef. [37],hasbeentrainedonsim- ulatedsamplescorrespondingtothedata-takingconditionsof 2015and2016.Theresponseiscalibratedseparatelyforelec- troncandidates,convertedphotoncandidatesandunconverted photon candidates. In data,small corrections are applied for the φ-dependent energy loss in the gaps between the bar- rel calorimeter modules (corrections up to 2%, in about 5%

ofthecalorimeteracceptance)andforinhomogeneitiesdueto sectorsoperatedatnon-nominalhighvoltage(correctionsbe- tween1%and7%,inabout2%ofthecalorimeteracceptance).

•^Theglobalcalorimeterenergyscaleisdeterminedinsituwith a largesample of Z→^{e+e−eventsselected inthe2015and} 2016datasets.The energyresponseindataandsimulationis equalisedbyapplying

η

-dependentcorrectionfactorstomatch theinvariant massdistributions ofZ→^{e+e−events.Theun-} certainty intheseenergyscalecorrection factorsranges from 0.02%to0.1%asafunctionof

η

,exceptforthebarrel–endcap transition region (1.37<|

η

|<1.52), where it reaches a few permille.Inthisprocedure,thesimulatedwidthoftherecon- structed Z boson mass distribution ismatched to the width observed indata by adding in the simulation a contribution totheconstanttermc oftheelectronenergyresolution, σE

E =

√a

E ⊕^b_E ⊕^{c.This constant termvariesbetween 0.7%and 2%}

for|

η

|<2.4 withanuncertaintyof0.03%–0.3%,exceptforthe barrel–endcap transition region, where the constant term is slightlyhigher(2.5%–2.9%)withanuncertaintyreaching0.6%.

Themainsourcesofsystematicuncertaintiesinthecalibration procedurediscussedinRef. [36] havebeenrevisited.Thesesources include uncertainties in the method used to extract the energy scalecorrectionfactors,aswellasuncertaintiesduetotheextrap- olationoftheenergyscalefromZ→^{e+e−eventstophotons,and} alsoto electrons withenergies differentfrom those produced in Z→^{e+e− decays. The latter arise from the} uncertainties in the linearityoftheresponseduetotherelativecalibrationofthedif- ferent gains used in the calorimeter readout, in the knowledge ofthe materialin front ofthecalorimeter (insideandoutsideof theID,referredtoasIDandnon-IDmaterialinthefollowing),in theintercalibrationofthedifferentcalorimeterlayers,inthemod- elling of the lateral shower shapes and in the reconstruction of photon conversions. The total calibrationuncertainty forphotons withtransverseenergy(ET)around60 GeV is0.2%–0.3%inthebar- reland0.45%–0.8%intheendcap. Theseuncertaintiesarecloseto thosequotedinRef. [36],buttypicallyabout10%larger.Thesmall increaseintheuncertaintyarisesmostlyfromalargeruncertainty intherelative calibrationofthefirst andsecondcalorimeterlay- erswithmuonsbecauseofaworseratioofsignaltopile-upnoise inRun 2 data. In the caseof electrons with ET around 40 GeV, the total uncertainty ranges between 0.03% and0.2% inmost of thedetectoracceptance.Forelectrons withET around10 GeV the uncertaintyrangesbetween0.3%and0.8%.

The accuracy of the energy calibration for low-energy elec- trons (5–20 GeV) is checked by computingresidual energy cali- bration corrections(after applyingthe correctionsextractedfrom theZ→^{e+e−sample)foran}independentsampleof J/ψ→^e+e− events.Theseresidualcorrectionfactorsarefoundtobe compati- blewithonewithinuncertainties.Asimilarcheckisperformedby computingresidualcorrectionsforphotonsinasampleofradiative Z bosondecays.Theyarefoundtobecompatiblewithonewithin uncertainties which are givenby the combinationof thestatisti- caluncertaintyoftheradiative Z bosondecayssample andofthe systematicuncertaintyfromtheextrapolationofthe energyscale fromelectronstophotons.

Systematic uncertainties in the calorimeter energy resolution arise from uncertainties in the modelling of the sampling term a/√

E andin the measurementof the constant termin Z boson decays,intheamountofmaterialinfrontofthecalorimeter,which affectselectrons andphotonsdifferently, andinthe modellingof thecontributiontotheresolutionfromfluctuationsinthepile-up fromadditionalproton–protoninteractions inthesame orneigh- bouringbunchcrossings.The uncertaintyoftheenergyresolution forelectrons andphotonswithtransverseenergybetween30and 60 GeV variesbetween5%and10%.

The identificationof photonsand the rejectionof background fromhadronsisbasedprimarilyonshowershapesinthecalorime- ter. The two levels ofselection, looseand tight, are described in Ref. [35].Tofurtherreducethebackgroundfromjets,twocomple- mentaryisolationselection criteriaare used,basedontopological clustersofenergydepositsinthecalorimeterandonreconstructed tracksinadirectionclosetothat ofthe photoncandidate,asde- scribedinRef. [24].

Electronsare identified usingalikelihood-based methodcom- bining informationfrom theelectromagnetic calorimeterandthe ID. As in the case of photons, electrons are required to be iso- lated using both the calorimeter-based and track-based isolation variablesasdescribedinRef. [38].

6. Statisticalmethods

The mass measurement is based on the maximisation of the profilelikelihoodratio [39,40]

(

mH

) =

^L

mH

, θ ( ˆˆ

mH

)

L

ˆ

mH

, θ ˆ ,

wherethe vectorsθˆ andmˆH denotetheunconditional-maximum likelihood estimates ofthe parameters ofthe likelihood function L,whileθˆˆ istheconditionalmaximum-likelihoodestimate ofthe parameters θ for a fixed value of the parameter mH. Systematic uncertainties and their correlations are modelled by introducing nuisanceparametersθ describedbylikelihoodfunctionsassociated withtheestimateofthecorrespondingeffect [6].

ThestatisticaluncertaintyofmH isestimatedbyfixing allnui- sanceparameterstotheirbest-fitvalues,allremainingparameters are thus left unconstrained. This approach yields a lower bound onthestatisticaluncertainty,whenthecombinationofthediffer- ent event categoriesdiscussed in the next sections is performed neglecting the differentimpact ofthesystematic uncertainties in eachcategory.Theupperboundonthetotalsystematicuncertainty isestimatedbysubtractinginquadraturethestatisticaluncertainty fromthetotaluncertainty.

Alternatively, the decomposition of the uncertainty into sta- tistical and systematiccomponents is performed using the BLUE method [41–43].Thetwoapproachesmayleadtodifferentresults from the decomposition of the uncertainty for a combination of

measurementswithsignificantanduncorrelatedsystematicuncer- tainties.

7. MassmeasurementintheH→^{Z Z∗}→⁴channel 7.1. Eventselection

Events are required to contain at least four isolated leptons (=^e,

μ

) that emergefroma commonvertex,formtwo pairs of oppositelychargedsame-flavourleptons.Electronsarerequiredto be within thefull pseudorapidity rangeofthe inner trackingde- tector (|

η

_|<2.47) andhavetransverseenergy ET>7 GeV, while muonsarerequiredto be withinthe pseudorapidityrangeofthe muon spectrometer (|

η

|<2.7) and have transverse momentum pT>5 GeV.The threehigher-pT (ET) leptons ineach quadruplet are required to pass thresholds of 20, 15, and 10 GeV, respec- tively.A detaileddescriptionof theeventselection can be found inRefs. [11,44].

Theleptonpairwithan invariantmassclosest tothe Z boson massineachquadrupletisreferredtoastheleadingdileptonpair, while the remaining pair is referred to as the subleading dilep- ton pair.The selectedeventsare split accordingtothe flavour of the leading and subleading pairs; ordered according to the ex- pected selection efficiency, they are 4

μ

,2e2

μ

,2

μ

2e,4e.Recon- structedphoton candidatespassing final-stateradiationselections aresearchedforinall theevents [45].Suchphotonsarefound in 4% of the eventsand their energy is includedin the mass com- putation.Inaddition,akinematicfitisperformedtoconstrainthe invariant mass of the leading lepton pair to the Z boson mass, improvingthem4 resolutionbyabout15% [7]. Theimprovement brought by the correction of the local tracker misalignments, as discussedinSection 4,isatthepercent levelforthem4 resolu- tionofsignal events.Aftereventselection,them₄ resolutionfor thesignal(atmH=^{125 GeV),estimatedwithaGaussianfitaround} the peak, is expected to be about 1.6, 1.8, 2.2 and 2.4 GeV for the4

μ

,2e2

μ

,2

μ

2eand4echannelsrespectively.Inthefitrange of 110<m4<135 GeV,123 candidateevents are observed.The yieldisinagreementwithanexpectationof107±^{6 events,53%of} whichareexpectedtobefromthesignal,assumingm_H=^{125 GeV.}

The dominantcontributionto thebackground isnon-resonant Z Z^∗ production(about84% ofthetotalbackgroundyield).Events withhadrons, orhadron decayproducts, misidentifiedasprompt leptonsalsocontribute (about15%).Eventsoriginatingfromt¯t+Z, Z Z Z, W Z Z, and W W Z production are estimated to contribute lessthan 1% of the total background.The residual combinatorial background,originating fromevents with additionalprompt lep- tons,wasfoundtobenegligiblysmall [44].

Theprecisionofthemassmeasurementisfurtherimprovedby categorisingeventswithamultivariatediscriminantwhichdistin- guishesthesignalfromtheZ Z^∗background.TheBDTdescribedin Ref. [7],basedonthesameinputvariables,istrainedonsimulated signaleventswithdifferentmassvaluessimultaneously (124,125 and126 GeV)and Z Z^∗ backgroundeventsthat passtheeventse- lection. For each final state, four equal-size exclusive bins inthe BDT response are used. This improves the precision of the m_H measurementinthe4decaychannelbyabout6%.

7.2. Signalandbackgroundmodel

Theinvariantmassineachcategoryisdescribedbythesumof asignalandabackgrounddistribution.

Non-resonant Z Z^∗ production is estimated using simulation normalisedto themostaccurate predictions andvalidatedinthe sidebands of the selected 4 mass range. Smaller contributions tothebackgroundfromtt¯+Z, Z Z Z, W Z Z andW W Z production

are alsoestimated usingsimulationwhile thecontributions from Z+jets, W Z, and t¯t production where one or more hadrons, or hadron decay products, are misidentified as a prompt lepton are estimatedfromdatausingminimalinput fromsimulationfollow- ing the methodologydescribed in Ref. [11]. Foreach contribution to the background, the probability density function (pdf) is esti- matedwiththekerneldensityestimation.

For the determination of the signal distribution, an approach based on the event-by-event response of the detector is em- ployed. The measured m4 signal distribution is modelledas the convolution of arelativistic Breit–Wignerdistribution, of4.1MeV width [27–30] and a peak at mH, with a four-lepton invariant mass response distributionwhich isderived event-by-eventfrom the expectedresponse distributionsoftheindividual leptons. The lepton energy responsedistributions are derived fromsimulation asafunctionoftheleptonenergyanddetectorregion.Thelepton energy response is modelled as a weighted sum of three Gaus- sian distributions. Foran observed event, them4 pdf isderived from the convolution of the response distributions of the four measured leptons. Thedirect convolutionofthe fourleptons dis- tributions, leading to3⁴=81 Gaussiandistributions,is simplified to a weighted sum of four Gaussian pdfs following an iterative mergingprocedureasperformedwiththeGaussian-sumfilterpro- cedure [46,47]. Anadditional correctionis appliedto remove the residualdifferenceswhicharise fromthe correlationbetweenthe lepton energy measurements introduced by the kinematic con- strainedfitontheleadingdileptonpairandtheBDTcategorisation ofevents.These arecorrected bya fitofscaling modifiersofthe reducedresponseparameters tothesimulatedfour-leptonresolu- tion.Thesemodifiersareabout0.1% forthemeansandupto10%

forthewidthsoftheGaussiansofthereducedresponse.

Finally, the mass of the Higgs boson mH is determined by a simultaneous unbinnedfitofsignal-plus-backgrounddistributions to dataover thesixteencategories.² The per-eventcomponentof thesignalpdfisaddedtothebackgrounddistributionwhichisin- tegrated over all kinematic configurations of the four final state leptons.IneachofthefourBDTcategories, thesignalyieldisfac- torised bya floatingnormalisationmodifier independentforeach BDT category. The measured Higgs boson mass depends on the lepton energy resolution and thelepton energyscale. Uncertain- ties inthese quantities are accountedforin the fitby Gaussian- distributed penalty termswhosewidths are obtainedfromauxil- iarydataorsimulationcontrolsamples.Theexpecteduncertainty, withmH=^{125GeV andproductionratespredictedbytheSM,for} adatasampleofthesizeoftheexperimentalset,evaluatedusing simulation-basedpseudo-experiments,is±⁰.35 GeV.

AvalidationwithdataisperformedwithZ→⁴eventstotest theperformanceofthemethodonaknownresonancewithsimilar topology.Inthistest,thepeakandwidthoftherelativisticBreit–

Wigner function are set to those of the Z boson. The measured Z boson mass was found to be 91.62±⁰.35 GeV including sta- tisticalandsystematicuncertainty. Theobserveduncertaintyisin agreement withthe expectationof±⁰.34 GeV,asevaluatedfrom simulation. The measured value is in agreement with the world averageof91.1876±⁰.0021 GeV [48].

Asanindependentcheck,thetemplatemethod [7] isalsoused to measure mH. The simulated distributions ofthe samples gen- erated for mH values between 110 and 130 GeV are smoothed with akernel densityestimate technique, and thenparametrised as a function ofm_H by means of aB-spline interpolationto ob- tainthesignalmodelforanyvalueofmH.Theexpectedstatistical uncertainty of mH obtained with the per-event method from a

2 FourperfinalstateforeachofthefourBDTcategories.

Fig. 1.(a)Invariantmassdistributionforthedata(pointswitherrorbars)showntogetherwiththesimultaneousfitresulttoH→Z Z^∗→4candidates(continuousline).

Thebackgroundcomponentofthefitisalsoshown(filledarea).Thesignalprobabilitydensityfunctionisevaluatedper-eventandaveragedovertheobserveddata.(b)Value of−^2lnasafunctionofmH forthecombinedfittoallH→^{Z Z∗}→⁴categories.Theintersectionofthe−^2lncurvewiththehorizontallineslabelled1σ and2σ providethe68.3%and95.5%confidenceintervals.

sampleequalinsizetotheexperimentaldatasetis,onaverage,3%

smallerthanthestatisticaluncertaintyobtainedwiththetemplate method.Bothmethodsarefoundtobeunbiasedwithinthestatis- ticaluncertaintyofthesimulatedsamplesusedofabout8 MeV on mH.

7.3.Results

The estimate of mH for the per-event and template methods isextracted witha simultaneous profile likelihoodfit to the six- teen categories. The free parameters of the fit are m_H, the nor- malisationmodifiers ofeach BDT category, andthe nuisance pa- rameters associated withsystematic uncertainties. The measured value of mH from the per-event method is found to be m_H^{Z Z∗}= 124.79±⁰.36(stat)±⁰.05(syst)GeV=¹²⁴.79±⁰.37 GeV.

The total uncertainty is in agreement with the expectation and is dominated by the statistical component. The root-mean- square of the expecteduncertainty due to statisticalfluctuations intheeventyieldsofeachcategorywasestimatedtobe40 MeV.

The p-value of theuncertainty beingas highor higherthan the observed value, estimated with pseudo-experiments, is found to be 0.47. The total systematic uncertainty is 50 MeV, the lead- ing sources beingthe muon momentum scale (40 MeV) andthe electron energy scale (26 MeV), with other sources (background modellingandsimulationstatistics)beingsmallerthan10 MeV.

Forthetemplate method,the totaluncertainty isfound to be +0.41

−0.39 GeV,larger by 35 MeV thanforthe per-event method.The observeddifference forthe mH estimates ofthe two methods is foundtobe0.16 GeV,whichiscompatiblewiththeexpectedvari- anceestimatedwithpseudo-experimentsandcorrespondstoaone sided p-value of0.19. Fig.1(a)showsthe m₄ distribution ofthe data together with the result of the fit to the H→^{Z Z∗}→⁴ candidateswhen usingtheper-event method.Thefit isalso per- formedindependentlyforeachdecaychannel,fittingallBDTcate- goriessimultaneously;theresultinglikelihoodprofileiscompared withthe combinedfitin Fig.1(b).Thecombinedmeasured value ofmH is foundto be compatible withthe value measured inde- pendentlyforeachchannel, withthelargestdeviationbeing1.4

σ

forthe2

μ

2echannelandtheothersbeingwithin1

σ

.

The Higgsbosonmassinthe four-leptonchannel isalsomea- suredby usinga profilelikelihood ratioto combinetheinforma- tionfromtheRun 1analysis [6],wheremH=¹²⁴.51±⁰.52 GeV, andtheRun 2analysis,keepingeach individualsignal normalisa- tionparameterindependent.Thesystematicuncertaintiestakento becorrelatedbetweenthetworunsarethemuonmomentumand electronenergyscales,whileallothersystematicuncertaintiesare considereduncorrelated. ThecombinedRun1andRun2resultis m^{Z Z}_H ^∗=¹²⁴.71±⁰.30(stat)±⁰.05(syst)GeV=¹²⁴.71±⁰.30 GeV.

The difference betweenthe measured values ofmH in the four- leptonchannelinthetworunsis m^{Z Z}_H ^∗=⁰.28±⁰.63 GeV,with thetworesultsbeingcompatible,withap-valueof0.84.

8. MassmeasurementintheH→

γ γ

channel

In the diphoton channel, the Higgs boson mass is measured fromthepositionofthenarrow resonantpeakinthemγ γ distri- butionduetotheHiggsbosondecaytotwophotons.Suchapeak isobserved overa large,monotonicallydecreasing,mγ γ distribu- tion from continuum background events. The diphoton invariant mass is computedfromthe measured photon energies andfrom their directions relative to the diphoton production vertex, cho- sen among all reconstructed primary vertex candidates using a neural-network algorithm based on trackand primary vertex in- formation,aswell asthedirectionsofthetwo photonsmeasured inthecalorimeterandinnerdetector [49].

Events are selected and divided into categories with differ- ent mass resolutions and signal-to-background ratios, optimised forthemeasurementofsimplifiedtemplatecross-sections [30,50]

and of production mode signal strengths of the Higgs boson in the diphoton decay channel. The event selection and classifica- tion are described in Ref. [24]. Apotential reduction of the total expected uncertainty by 4% could have been obtainedusing the sameeventcategorieschosenforthemassmeasurementwiththe Run 1 data [7]. Giventhe small expectedimprovement,a choice wasmadetousethesamecategorisationforthemeasurementof themassandoftheproductionmodesignalstrengths.

Fig. 2.(a)Invariantmassdistributions(circles)ofsimulatedH→γ γeventsreconstructedintwocategorieswithoneofthebest(“ggH0JCen”:opencircles)andoneofthe worst(“ggH0JFwd”:solidcircles)experimentalresolutions.Thesignalmodelderivedfromafitofthesimulatedeventsissuperimposed(solidlines).(b)Diphotoninvariant massdistributionofallselecteddataevents,overlaidwiththeresultofthefit(solidredline).Bothfordataandforthefit,eachcategoryisweightedbyafactorln(1+S/B), whereSandBarethefittedsignalandbackgroundyieldsinamγ γ intervalcontaining90%oftheexpectedsignal.Thedottedlinedescribesthebackgroundcomponentof themodel.Thebottominsetshowsthedifferencebetweenthesumofweightsandthebackgroundcomponentofthefittedmodel(dots),comparedwiththesignalmodel (blackline).(Forinterpretationofthecoloursinthefigure(s),thereaderisreferredtothewebversionofthisarticle.)

8.1. Eventselectionandcategorisation

Afteraninitialpreselection,describedinRef. [24],requiringthe presenceofatleasttwolooselyidentifiedphotoncandidateswith

|

η

_|<1.37 or1.52<|

η

_|<2.37, eventsareselected iftheleading and the subleading photon candidates have ET/mγ γ >0.35 and 0.25 respectively, and satisfy the tight identification criteria and isolation criteria based on calorimeter and tracking information.

Only events with invariant mass of the leading and subleading photonintherange105 GeV<mγ γ<160 GeV arekept.

The events passing the previous selection are then classified, accordingtothepropertiesofthetwoselectedphotonsandofjets, electrons,muonsandmissingtransversemomentum,into31mu- tuallyexclusivecategories [24].Themostpopulatedclass,targeting gluon–gluon fusionproductionwithoutreconstructedjets, issplit intotwocategoriesofeventswithverydifferentenergyresolution:

thefirst(“ggH 0JCen”) requiresbothphotonsto have|

η

_|<0.95, whilethesecond(“ggH0JFwd”)retainstheremainingevents.

8.2. Signalandbackgroundmodels

For each category, the shape of the diphoton invariant mass distribution of the signal is modelled with a double-sided Crys- tal Ballfunction [51], i.e.a Gaussian function in thepeak region withpower-lawfunctionsinbothtails.Thedependenceofthepa- rametersontheHiggsboson massmH isdescribed by first-order polynomials,whoseparametersarefixedbyfittingsimultaneously all thesimulatedsignal samples generatedfordifferentvalues of mH.

Thequantity

σ

68,definedashalfofthesmallestrangecontain- ing68%oftheexpectedsignalevents,isanestimate ofthesignal mγ γ resolutionandformH=^{125 GeV itrangesbetween1}.41 GeV and2.10 GeV dependingon the category, whileforthe inclusive caseitsvalueis1.84 GeV.Fig.2(a)showsanexampleofthesignal modelfora categorywithone ofthebest invariantmass resolu- tionsandforacategorywithoneoftheworstresolutions.

The expected signal yield is expressed as the product of in- tegrated luminosity,productioncross-section, diphoton branching ratio,acceptanceandefficiency.Thecross-sectionisparameterised asafunctionofmH separatelyforeachproductionmode.Similarly, thebranchingratioisparameterisedasafunctionofm_H.Theprod- uct of acceptanceand efficiency is evaluated separately for each productionmode usingonlythe sampleswithm_H =^{125 GeV.Its} dependenceonthemassisweak(relativevariationbelow1%when varying theHiggsbosonmassby ±^{1 GeV)andisthus neglected.}

The cross-sectionsarefixed totheSMvaluesmultipliedbya sig- nalmodifierforeachproductionmode:

μ

ggF,

μ

VBF,

μ

V H and

μ

tt H¯ . The expected yield form_H =125 GeV varies betweenabout one eventincategoriessensitivetorareproductionmodes(t¯t H,t H)to almost 500eventsinthemostpopulatedeventcategory (“ggH0J Fwd”).

Thebackgroundinvariantmassdistributionofeachcategoryis parameterisedwithanempiricalcontinuousfunctionofthedipho- tonsysteminvariantmassvalue.Theparametersofthesefunctions arefitteddirectlytodata.Thefunctionalformusedtodescribethe backgroundineachcategory ischosen amongseveralalternatives accordingtothethreecriteriadescribedinRef. [24]:(i)thefitted signalyieldinatestsamplerepresentativeofthedatabackground, built by combining simulation and control regions in data, must beminimised;(ii)the

χ

² probabilityforthefitofthisbackground control sample must be larger than a certain threshold; (iii) the qualityofthefittodatasidebandsmustnotimprovesignificantly whenaddinganextradegreeoffreedomtothemodel.Themodels selectedbythisprocedureareexponentialorpower-lawfunctions with one degree of freedom for the categories with few events, whileexponentialfunctionsofasecond-orderpolynomialareused fortheothers.

From the extrapolation of a background-only fit to the side- bands of the mγ γ distribution in data, excluding events with 121 GeV<mγ γ<129 GeV,theexpectedsignal-to-backgroundra- tioinamγ γ windowcontaining90%ofthesignaldistributionfor mH =125 GeV varies between2% in the “ggH 0JFwd” category and 100% in a high-purity, low-yield (about 12 events) category

targetingH+2jet,VBF-likeeventswithlow transversemomentum oftheH+2jetsystem.

8.3.Systematicuncertainties

The main sources of systematic uncertainty in the measured Higgsboson mass in the diphoton channel are the uncertainties in the photon energy scale (PES), the uncertainty arising from the background model, and the uncertainty in the selection of the diphoton production vertex. They are described in detail in Ref. [24].

ForeachsourceofuncertaintyinthePESdescribedinSection5, thediphoton invariant massdistribution for each category is re- computedaftervaryingthephotonenergybyitsuncertaintyandis thencomparedwiththenominaldistribution.Thesuminquadra- tureofthepositiveornegativeshiftsofthemγ γ peakpositiondue tosuchvariationsrangesfrom±^{260 MeV inthe“ggH0JCen”cat-} egoryto ±^{470 MeV in the“jet BSM” category, whichrequiresat} leastonejetwithpT>200 GeV.AllthePESeffectsareconsidered asfullycorrelatedacrosscategories.

Theuncertaintyduetothebackgroundmodellingis evaluated following the procedure described in Ref. [7]. The expected sig- nalcontributionaspredictedbythesignal modelisaddedtothe backgroundcontrolsample.ThebiasintheestimatedHiggsboson massfromasignal-plus-backgroundfittothetestsample relative totheinjectedmassisconsideredasasystematicuncertaintydue tothebackgroundmodelling.Itsvalueisaround±^{60 MeV forthe} mostrelevantcategoriesforthe massmeasurement. Inthe other categoriesitcanassumelarger values,whicharecompatiblewith statisticalfluctuationsofthe backgroundcontrol sample. Forthis reasonthis systematic uncertainty is ignored in the poorly pop- ulatedtt H¯ categories, which givea negligiblecontribution tothe massmeasurement.Thissystematicuncertaintyisassumedto be uncorrelatedbetweendifferentcategories.

The systematic uncertainty related to the selection of the diphotonproduction vertexis evaluated using Z→^{ee events, as} describedinRef. [7].Anexpecteduncertaintyof±^{40 MeV inm}H isused for all the categoriesand assumedto be fully correlated acrossdifferentcategories.

Systematicuncertaintiesinthediphotonmassresolutiondueto uncertainties inthe photon energy resolutionvary between±^6%

(forthe “ggH0J Cen”category)and11% (for the“jet BSM” cate- gory),andare expectedto have anegligible impact onthe mass measurement.

Systematicuncertainties in the yield and in the migration of eventsbetweencategoriesdescribed inRef. [24] haveanegligible impactonthemassmeasurement.

Theuncertainty duetothe signal modellingisevaluated sim- ilarlyto thatdueto thebackground modelling. Asample isbuilt usingtheexpectedbackgrounddistributionandthesimulatedsig- nal events atmH =^{125 GeV. The bias in the fitted Higgs boson} massisconsidered asasystematicuncertaintyandisassumedto becorrelatedbetweendifferentcategories.Therelativebiasisbe- low10⁻⁴ inmostofthecategories,andatmostafewtimes10⁻⁴ intheothercategories.

8.4.Results

The Higgs boson mass in the diphoton channel is estimated witha simultaneous binned maximum-likelihood fit to the mγ γ distributionsoftheselectedeventcategories.Ineachcategory,the distribution is modelled witha sumof the background and sig- nalmodels.The freeparametersofthefitaremH,thefoursignal strengths, the number ofbackground events and the parameters

describing the shape of the background invariant mass distribu- tion ineach category,andall the nuisanceparameters associated with systematicuncertainties. Fig. 2(b) showsthe distribution of thedataoverlaidwiththeresultofthesimultaneousfit.Allevent categories are included. For illustration purposes, events in each categoryareweightedbyafactorln(1+^S/B),whereS andBare thefittedsignalandbackgroundyieldsinamγ γ intervalcontain- ing90%ofthesignal.

The measuredmassof theHiggsbosonin thediphotonchan- nel ismγ γ

H =¹²⁴.93±⁰.21 (stat)±⁰.34 (syst) GeV= ¹²⁴.93± 0.40 GeV wherethefirsterroristhestatisticaluncertaintywhile the second is the total systematicuncertainty, dominatedby the photonenergyscaleuncertainty.

Assuming signal strengths asin theSM andthesignal model determined from the simulation, the expected statistical uncer- taintyis0.25GeV andtheexpectedtotaluncertaintyis0.41GeV, witha root-mean-square, estimatedfrom pseudo-experiments, of about 40 MeV. Compared to the expectation, the slightly larger systematicuncertaintyandsmallerstatisticaluncertaintyobserved indataareduetoalowerthanexpectedsignalyieldinsomecat- egories with large expected yield andsmall photon energyscale uncertainty, andtothe fittedresolution indatabeinga few per- centbetterthaninthesimulation(butstillagreeingwithitwithin onestandarddeviation).

To check if the measurement is sensitive to the assumption aboutthe splittingofthe productionmodes, themeasurement is repeatedusingone commonsignalstrength forallthe processes.

A small shift of the measured mH by 20 MeV is observed. The massmeasurement isalsoperformedby allowing theoverallsig- nalyieldineachanalysiscategorytofloatindependentlyinthefit.

ThemeasuredvalueofmH changesbylessthan30 MeV.

Other checks targetingpossiblemiscalibration dueto detector effectsforsomespecificcategoryofphotonsareperformedbypar- titioning theentire datasample intodetector-oriented categories, different from those used for the nominalresult, and determin- ingtheprobabilitythatm_H measuredinoneofthesecategoriesis compatiblewiththeaveragemH fromtheother categories.Afirst categorisationisbasedonwhetherthephotonsarereconstructed as converted or not, a second is based on the photons’ impact pointsinthecalorimeter(eitherinthebarrelregion,|

η

|<1.37,or intheendcapregion,|

η

_|>1.52),andathirdisbasedonthenum- berofinteractionsperbunchcrossing.Foreachofthesecategories anewbackgroundmodel,anewsignalmodelandnewsystematic uncertaintyvalues are computed. Foreach categorythe compati- bility of its mH value withthe combined mH value is testedby consideringasanadditionallikelihoodparameterthequantity _i equaltothedifferencebetweenthatcategory’smH valueandthe combinedvalue.Novalueof isignificantlydifferentfromzerois found.Asimilartestisperformedtoassesstheglobalcompatibil- ityofallthe differentcategorieswitha commonvalueofmH.In thethreecategorisationsconsideredthesmallestglobalp-valueis 12%.The sameprocedureisapplied tothecategoriesused inthe analysis:thesmallestp-valuecomputedonsinglecategoriesis7%

whiletheglobalp-valueis94%.

AcombinationoftheHiggsbosonmassmeasuredinthedipho- ton channel by ATLAS in Run 1, 126.02±⁰.51 GeV [6], and in Run 2 is performed using a profile likelihood ratio. The signal strengths are treated asindependent parameters. The systematic uncertainties consideredcorrelatedbetweenthetwoLHC runpe- riods are mostof the photon energy scale andresolution uncer- tainties and those in the pile-up modelling, while all the other systematicuncertainties are considered uncorrelated. The photon energy calibration uncertainties that are treated as uncorrelated between the two LHC data-taking periods are a few uncertain- ties included only in the Run 2 measurement, the uncertainty

Fig. 3.Thevalueof−2lnasafunctionofmHfor(a)H→γ γ,H→Z Z^∗→4channelsandtheircombination(red,blueandblack,respectively)usingRun 2dataonlyand for(b)Run 1,Run 2andtheircombination(red,blueandblack,respectively).Thedashedlinesshowthemassmeasurementuncertaintiesassumingstatisticaluncertainties only.

in the photon energy leakage outside the reconstructed clus- ter, whose measurement is limited by the statisticalaccuracy of Z→

γ

,andthe uncertaintyinthe electromagneticcalorimeter response non-linearity, which is estimated with different proce- duresinthe two LHCrun periods. Theresult ismγ γ

H =¹²⁵.32± 0.19 (stat)±⁰.29 (syst) GeV = ¹²⁵.32±⁰.35 GeV. The differ- encebetweenthe measured valuesofm_H in the diphotonchan- nel in the two LHC run periods is mγ γ

H =¹.09±⁰.46 (stat)± 0.34 (syst) GeV = ¹.09±⁰.57 GeV.The probabilitythat thetwo resultsarecompatibleis5.1%.

9. Combinedmassmeasurement

The Higgsboson mass ismeasured by combining information fromboththeH→^{Z Z∗}→⁴andH→

γ γ

channels.Thecorrela- tionsbetweenthesystematicuncertaintiesinthetwochannelsare accountedforintheprofilelikelihoodfunction.The mainsources of correlated systematic uncertainty include the calibrations of electronsandphotons, thepile-upmodelling, andthe luminosity.

Signalyieldnormalisationsaretreatedasindependentfreeparam- etersin thefitto minimisemodel-dependentassumptions inthe measurementoftheHiggsbosonmass.

ThecombinedvalueofthemassmeasuredusingRun 2datais mH=¹²⁴.86±⁰.27 GeV. Assuming statistical uncertainties only, the uncertainty in the combined value is ±⁰.18 GeV. The cor- responding profile likelihood, for the two channels andfor their combination, is shownin Fig. 3(a). This result is in good agree- mentwiththeATLAS+CMSRun 1measurement [6],mH=¹²⁵.09± 0.24 GeV.

ThecombinedmassmeasurementfromtheATLASRun 1(m_H= 125.36±⁰.41 GeV)andRun 2resultsismH=¹²⁴.97±⁰.24 GeV.

Assuming statistical uncertainties only, the measurement uncer- tainty amountsto0.16 GeV.Fig.3(b)showsthevalue of−^2ln asafunctionofmH forthetwochannelscombined,separatelyfor theATLASRun 1andRun 2datasets,aswell asfortheircombi- nation.

Thecontributionsofthemainsourcesofsystematicuncertainty tothecombinedmassmeasurement,usingbothATLASRun 1and Run 2data,aresummarisedinTable1.Theimpactofeachsource ofsystematicuncertaintyisevaluated startingfromthe contribu- tionofeachindividualnuisanceparametertothetotaluncertainty.

Thiscontributionisdefinedasthemassshiftδm_H observedwhen

Table 1

MainsourcesofsystematicuncertaintyintheHiggsbosonmassmHmeasuredwith the 4andγ γ finalstatesusingRun 1and Run 2data.Thesuminquadrature oftheindividualcontributionsisnotexpectedtoreproducethetotalsystematic uncertaintyduetothedifferentmethodologiesemployedtoderivethem.

Source Systematic uncertainty inmH[MeV]

EM calorimeter response linearity 60

Non-ID material 55

EM calorimeter layer intercalibration 55

Z→eecalibration 45

ID material 45

Lateral shower shape 40

Muon momentum scale 20

Conversion reconstruction 20 H→γ γbackground modelling 20 H→γ γvertex reconstruction 15

e/γenergy resolution 15

All other systematic uncertainties 10

re-evaluating the profilelikelihood ratioafterfixing the nuisance parameter inquestion toits best-fitvalue increasedordecreased by one standard deviation, while all remainder nuisanceparam- eters remain free to float. The sum in quadrature of groups of nuisance parameter variations gives the impact of each category of systematic uncertainties. The nuisance parameter values from theunconditionalmaximum-likelihoodfitare consistentwiththe pre-fitvalueswithinonestandarddeviation.

The probability that the mH results from the four measure- ments(inthe4and

γ γ

finalstates,usingRun 1orRun 2ATLAS data) are compatible is 12.3%. Due to the impact of the corre- latedsystematicuncertainties,thecorrelation betweenm_H inthe H→

γ γ

channelover thetwo runsis23%. Theresidual correla- tion between H→^{Z Z∗}→⁴ and H→

γ γ

is typically 1%. The resultsfromeachofthefourindividualmeasurements,aswellas various combinations,along withtheLHC Run 1result, aresum- marisedinFig.4.

The combination of the four ATLAS measurements using the BLUE approach as an alternative method, assuming two uncor- related channels,³ is found to be mH =¹²⁴.97± ⁰.23GeV=

3 The combinationofthetwo LHCrun periodsfor eachchannelwasusedas input.